David Moyes hailed his Everton players for going "toe-to-toe" with Manchester United as they gained a draw at Old Trafford after twice trailing by two goals.

"I am extremely proud," he said. "You won't have enough room to write about the game, so many things happened. I thought it was a great game. I just thought our players were terrific from the first minute to the last. I'm disappointed that people would actually question the character of Everton – that's a bit insulting. We made a couple of chances early doors and didn't take them but we kept going and eventually got in front and rightly so.

"Manchester United's quality is always going to be something you have to worry about all the time and they scored some really good goals. But we kept at it and deservedly got the draw."

After Nikica Jelavic's 33rd-minute opener, Wayne Rooney equalised ahead of the interval before second-half goals from Danny Welbeck and Nani gave United a 3-1 lead. Marouane Fellaini's 67th-minute goal was answered by Rooney but then Jelavic's second and Steven Pienaar's 85th-minute equaliser secured a point for Everton.

Moyes admitted the task to lift his players after Everton's last-minute defeat by Liverpool in their FA Cup semi-final at Wembley had been difficult. "I think after anybody loses a semi-final to their local rivals it's tougher to take, so yeah there was a little bit of that," he said. "But the message today was that we were going to try and beat Manchester United. We were going to go toe-to-toe. We didn't back off. It was a wee bit to say, 'Hey, we're not that bad a team.' We've been a very good team since January. From our point of view we reminded people that we're still here."

Moyes also criticised Michael Jones, the referee, for stopping play when Jonny Evans went down but not when Pienaar was felled in the move that led to Welbeck's goal. "I thought it was rubbish," he said. "He stopped play for Jonny Evans. They [referees] can do what they want, they can make their minds up and I thought he made his own rules up. Steven Pienaar is down and you would think if he was consistent he would even it up. He never did it and they scored from it. I thought he was poor, I have to say."